June Barrow-Green
The 18th and 19th centuriesThe first woman in the modern period to make a substantial contribution to mathematics was the Italian Maria Agnesi who in 1748 published one of the earliest textbooks on the differential and integral calculus, Instituzioni Analitiche, which she originally wrote in order to instruct her younger brothers. Written in the vernacular (which was unusual in the period), the book was accessible to a broad audience and an important contribution to the spread of the calculus in Italy. Two years after the book's publication, she was appointed to the chair of mathematics in Bologna on the recommendation of the Pope, Benedict XIV, but she never took up the position. Agnesi did not even go to Bologna although her name remained on the rolls of the university. Instead she devoted her life to works of charity.4Much has been written on the content and reception of Agnesi's text but I want to draw attention only to some remarks made by the French historian of mathematics, Jean-Etienne Montucla, as they are illustrative of contemporary views about women mathematicians. Montucla, who was writing at the end of the 18th century, was complementary about the book but nevertheless rued the fact that there was no translation of it by one of the French women mathematicians-he didn't say who he had in mind-thereby implying that he believed there to be a difference between the way men and women approach and study mathematics.5 At the same time, he was also astonished that a woman-or as he put it "a person of a sex that seems so unfit to tread the thorny paths of abstract sciences" [3]-could penetrate so deeply into the calculus, thereby reinforcing the notion of the general unsuitability of women for mathematics.Agnesi, along with a number of other women in the 18th and early 19th century, such as Émilie du Châtelet (1706-1749), Ada Lovelace (1815-1852) and Mary Somerville (1780-1872), all of whom made lasting and significant contributions to mathematics, were not prevented from doing mathematics, in fact sometimes rather the opposite. For example, Lovelace, today renowned for her remarkable paper which explained the principles of Charles Babbage's analytical engine [4], was encouraged by her mother to study mathematics with Augustus De Morgan.6 Something these women all had in common was that they came from a social class which gave them the time and the opportunity to discuss mathematics (and natural philosophy) with men on equal terms. Both Somerville and Lovelace attended Babbage's scientific soirées and together they frequently called on him in order to see and to discuss his analytical engine.That Élisabeth Ferrand (1700-1752), an important influence on Abbé de Condillac and a friend of Alexis Claude Clairaut, chose a page from Voltaire's influential 4 For a discussion of Agnesi's life, see Paula Findlen's excellent essay review [2]. 5 There was a French translation by a man, Pierre Thomas d'Antelmy, which appeared in 1775. An English translation by John Colson appeared in 1801. It was a mi...